Arbitrary Spin Representations in de Sitter from dS/CFT with Applications to dS Supergravity

TL;DR

This work addresses the problem of classifying unitary, arbitrary‑spin representations in de Sitter space, including partially massless cases, by a group‑theoretic approach that employs a bulk‑to‑boundary intertwiner to Euclidean boundary conformal data in ${\mathbb R}^n$. The method yields explicit relations between bulk mass $m^2$ and conformal weight $\Delta_s$, and it identifies depth‑$t$ tunings $\Delta_s = n+s-t-1$, $m^2=(t-1)(2s-3+n-t)$ that realize partially massless gauge invariances for bosons (and analogous tunings for fermions). A concrete framework is developed for scalars and higher spins, connecting bulk dynamics to boundary conformal representations via the Casimir condition $\mathcal{C}_2=-\Delta_s(\Delta_s-n)-s(s+n-2)$ and the bulk equation of motion, with explicit bulk‑to‑boundary propagators. The paper also reassesses the prospects for constructing a consistent de Sitter supergravity within the intrinsic horizon, arguing that while free fields can be unitary inside the horizon, global obstructions and reality conditions for fermionic masses pose significant challenges. Overall, the work provides a unified, dimension‑independent picture of high‑spin fields in de Sitter space and informs holographic and cosmological supergravity discussions.

Abstract

We present a simple group representation analysis of massive, and particularly ``partially massless'', fields of arbitrary spin in de Sitter spaces of any dimension. The method uses bulk to boundary propagators to relate these fields to Euclidean conformal ones at one dimension lower. These results are then used to revisit an old question: can a consistent de Sitter supergravity be constructed, at least within its intrinsic horizon?

Figures (1)

• Figure 1: Cosmological phase diagrams for partially massless Bose and Fermi fields depicting strictly massless and maximal depth partially massless tunings. All other lines with partially massless gauge invariances appear between these.